Precession in a 45 m high metalic antenna tower

[luislb]

TL;DR Summary

In the top of th 45 m high mettalic tower is fixed an radar antenna + motor, the antenna pedestal is fixed in the geometrical centre of the tower (section 3x3), although the pedestal where the antenna is placed is in the geometric centre of the platform at 45 m, there is an excentricity between the centre of rotation and the centre of gravity of the tower. In this case there is a precession induced by the antenna in the whole angle mettalic tower.

1- the antenna + motor weights about 400 Kg (the helix weights about 170 Kg and has adiameter of 6.28 m, and the motor of the antenna weights 230Kgs), there is an excentricity between the centre of gravity of the antenna + motor and the centre of rotation of the anetnna which is 42 mm in the yy direction.

2- After the antenna is fixed to a pedestal in the top of the tower (45 m) the centre of gravity of the whole structure (tower + antenna) is about 5 mm in the xx direction, and 23.84 mm, the centre of rotation of the antena is 148 mm in the yy direction (see scheme).

3- The free force given by:
FS=Mr x ω^2 x e; eurocode 1 -parte 3, pag 39

MR- mass of the rotor
ω - angular velocity
e- excentricity

The angular velocity is 60 rpm, the excentricity is about 171.84 mm, what is the MR, if the antenna is fixed to the tower?

4- Because of the excentricity i discribed, there are a precession motion induced by the rotating atenna, what is the magnitude of this forces, and how they afect the tower? ( the angular moment of the helix of the antenna L= I ω, the torque is given by r x mg the velocity of the precession is given by r x mg/I.ω rad/s.)

5- In a simplified way the antenna + motor we can consider that the antenna is rotating fixed to a plate, and the are excentricity between the centre of rotation and centre of gravity induces precession what forces occur in this case, (see picture vertical axis), there is a relation between the a rotating vertical axis and horizontal axis( see pecture horizontal axis)?

6- If i formulate the problem through the conservation of the linear moment, between the L before ( antenna+ motor ) = L after (antenna + motor + tower) is it appropriated?thanks

 

[JBA]

Is this an actual observed precession of an installed facility; or, a theoretical problem statement.
If the antenna Cg is directly at the center of its rotation in both horizontal axes and it is fully rotationally balanced then it should not introduce any lateral precession forces on the structure due directly to its mass rotation regardless of its lateral eccentricity from the tower CL.

 

[luislb]

Thank you for your help, it´s actually a observed precession on a already installed mettalic tower, but it´s also objet of a study for my thesis in civil engineering in order to understand why this precession ( oscillation occurs in the tower, when the radar antenna is in motion).
The tower oscillation as a precession motion observed in loco, and may be amplified due to the action of the wind, i think.

The antenna as two components the helix and the motor, and as you can see in the pictures, the centre of rotation CR of the antenna is displaced about 42 mm in the yy direction to the centre of gravity CG.

This antenna is placed in the pedestal located in the geometric centre of the tower GC, and when fixed to the tower there is an excentricity of the whole structure that is about 178 mm between the CR of the antenna and the CG of the whole structure ( antenna+ motor pedestal and tower).

1- There is a free force (unbalanced force) which is calculated for the formula that i mencioned in the first post, and it appears in eurocode, my doubt is, since the tower and the antenna are fixed together what mass do i consider in the formula?

2- Geometricaly there is a excentricity between the CR of the antenna and the CG of the whole structure, which causes precession or not?

thanks

 

[JBA]

With regard to the wind issue, my primary thought was that the effect could be due to the eccentric loading on the antenna's rotating arms due to wind. When the arms are parallel to the wind there is no imbalance force; but, when the arms are perpendicular to the wind then there is a drag force on both arms but more so on the arm that is turning into the wind than the other turning away from the wind. A the same time, due to the antenna eccentricity from the tower C/L, when the wind is perpendicular to the offset of the antenna from the tower CG there will also be a twisting moment on the tower, especially when the wind is directed at the outer approaching antenna arm.

Note: The below is just my thoughts and has no supporting evidence of any kind to confirm its overall approach to this problem.

With regard to items 1. and 2., my first inclination to analyzing the precession effect on the tower assembly is to break the analysis into two parts:
First, determine the FS from what must be some e (eccentricity) of the antenna CG from its center of rotation, or vertical tilt along its length relative to the axis of rotation. (as I stated above without that, there cannot be any rotating mass oscillating force on the tower assembly due to the antenna's rotation) using that e, the mass of the rotating antenna as MR and 60 rpm for the angular velocity in the equation.
Next, use that same formula reconfigured to solve for the e (eccentricity) of the tower using that FS, the tower assembly as the MR and the 60 rpm as the angular velocity.
One thing that I am unsure about in this calculation is whether to increase the FS based upon the ratio of the height of the antenna to the height of the CG of the tower assembly for this calculation.
At the same time, if possible, I would analyze the tower as a cantilever beam with original FS as an end load to see if there is any correlation the eccentricity calculated by the above method.
Additionally, while I would expect the natural frequency of the tower assembly to be much lower than 60 cps, it would be worthwhile to calculate the natural frequency of the tower assembly to be sure there is no amplifying effect from the 60 cps to tower natural frequency ratio on the FS.

 

[tech99]

Maybe the wind resistance alters as the antenna rotates. This will excite the tower at 1 or 2 Hz. Does it do it in calm weather?

 

[luislb]

i didn´t measure the osillation (circular) but in the ground can be easily seen, the wind normally is from a constant direction, the antenna is located in shore next to the sea. In calm weather also oscillate.

 

[JBA]

All things considered, the most likely potential cause of the precession, if it is not a wind effect, is that either the antenna has not been carefully longitudinally balanced about the antenna center point or the drive shaft mounting is not exactly centered longitudinally on the antenna, either one resulting in an rotational force imbalance.

 

[Baluncore]

JBA has covered most points.
I would certainly measure the resonant frequency of the tower when the radar is not rotating. Guessing is not good enough.

If the tower is resonant close to the 60 RPM unbalance, = 1 Hz frequency, then you must change the resonant frequency of the structure. That could be done by changing the mass at the top of the tower, or by changing the height of the tower by one module, up or down.

It would also be possible to dampen the resonance by hanging a short pendulum in the top of the tower, or by having a circular tank of liquid that will dampen that resonance.

As the antenna rotates it presents maximum wind drag, twice per cycle. That could excite a 2 Hz resonance in the tower. I would expect an amplitude proportional to the square of the wind speed. Maybe that resonance is present, but is now hidden by the 1 Hz cyclic movement.

 

[berkeman]

1- the antenna + motor weights about 400 Kg (the helix weights about 170 Kg and has adiameter of 6.28 m, and the motor of the antenna weights 230Kgs), there is an excentricity between the centre of gravity of the antenna + motor and the centre of rotation of the anetnna which is 42 mm in the yy direction.

Why is there an eccentricity? That sounds like a design defect. Have you talked with the manufacturer of this subsystem about it? Or is this a home-brew combination of the motor + antenna?

And after you get the mechanical assembly balanced better, you could still consider a cylindrical radome structure on the top of the tower to eliminate the wind effects, IMO.

https://fccid.io/png.php?id=2769752&page=7

 

[berkeman]

If the tower is resonant close to the 60 RPM unbalance, = 1 Hz frequency, then you must change the resonant frequency of the structure. That could be done by changing the mass at the top of the tower, or by changing the height of the tower by one module, up or down.

It would also be possible to dampen the resonance by hanging a short pendulum in the top of the tower, or by having a circular tank of liquid that will dampen that resonance.

Do you have access to any of the land around the tower? Like, is it within some larger fenced-off enclosure with other equipment? If so, consider using 4 guy wires from the top of the antenna out and down to the ground to limit/eliminate the movement.

 

[luislb]

With regard to the wind issue, my primary thought was that the effect could be due to the eccentric loading on the antenna's rotating arms due to wind. When the arms are parallel to the wind there is no imbalance force; but, when the arms are perpendicular to the wind then there is a drag force on both arms but more so on the arm that is turning into the wind than the other turning away from the wind. A the same time, due to the antenna eccentricity from the tower C/L, when the wind is perpendicular to the offset of the antenna from the tower CG there will also be a twisting moment on the tower, especially when the wind is directed at the outer approaching antenna arm.

Note: The below is just my thoughts and has no supporting evidence of any kind to confirm its overall approach to this problem.

With regard to items 1. and 2., my first inclination to analyzing the precession effect on the tower assembly is to break the analysis into two parts:
First, determine the FS from what must be some e (eccentricity) of the antenna CG from its center of rotation, or vertical tilt along its length relative to the axis of rotation. (as I stated above without that, there cannot be any rotating mass oscillating force on the tower assembly due to the antenna's rotation) using that e, the mass of the rotating antenna as MR and 60 rpm for the angular velocity in the equation.
Next, use that same formula reconfigured to solve for the e (eccentricity) of the tower using that FS, the tower assembly as the MR and the 60 rpm as the angular velocity.
One thing that I am unsure about in this calculation is whether to increase the FS based upon the ratio of the height of the antenna to the height of the CG of the tower assembly for this calculation.
At the same time, if possible, I would analyze the tower as a cantilever beam with original FS as an end load to see if there is any correlation the eccentricity calculated by the above method.
Additionally, while I would expect the natural frequency of the tower assembly to be much lower than 60 cps, it would be worthwhile to calculate the natural frequency of the tower assembly to be sure there is no amplifying effect from the 60 cps to tower natural frequency ratio on the FS.

Thank you very much JBA for you ideas, they are very interesting, that will help me to understand better the problem.It took a bit to understand, because my english is nor very good.

Regarding the wind force, in the case of the drag force, that produces imbalanced force, can be calculated through the resultant force, from the equilibrium of forces. How is the equilibrium forces?

The twisting moment only occurs when the arms of the antenna, are in the direction of the CR and the CG of the Tower?

FS
in he first step, i use only the mass od the arms to calculate Fs,that is the MR=170Kg and e (that is the distance between the CR and The CG of the antenna)?

in the second step i consider the mass of the whole strucutre assembled weights 10544 Kg´s, and the e is 178mm ( distance between the CR of the antenna and the CG of the whole structure)?

in can do that analisys what is the original FS teh first you mentioned, what is the correlation you want to see i don't understand?

you´re the natural frequency of the tower is 1.54 Hz, much lower tha the 60 cps, it´s a mettalic tower made with angle profiles, S355 and S275.

I´m preforming a dinamic analisys where i consider 3 scenarios

1- FS with MR=170 Kg, aplly the force in the CR of the antenna and made the force varying direction from 22.5 to 22.5 until reach the 360º, the i preform a harmonic dinamic analises analysis. I got 2.4 cm of siplacement

2- The FS is 400 Kg, located in the CR, and preform a harmonic dinamic analisys where the velocity od the harmonic analisys is the 60 rpm. I got 5.7 max displacement.

3- The Fs1 is 400 apllied on the CR of the antena, and another Fss with the mass of platform at 45 m, with the mass MR of the platforma, and the force aplied on the GC of the platform and then prefrom a dinamic harmonic analisys, in the same way of the other scenarios. I got 6.8 max displacement.

What do you think of this method?

thank you very much

The

 

[luislb]

All things considered, the most likely potential cause of the precession, if it is not a wind effect, is that either the antenna has not been carefully longitudinally balanced about the antenna center point or the drive shaft mounting is not exactly centered longitudinally on the antenna, either one resulting in an rotational force imbalance.

That is truth they didn´t place the antenna is the best place to reduce the displacements, but even if the had had that care there is allays uncertain because in the realitty the centre of gravity is hard to define, because there are variable you can´t control like the imperfectiond of the material, and the constance of the sections, or even the distribution of the weight.
To reduce these effects , yhe ideia is to place in the top platform a water tank, TLD ( tunned liquid damper), using the method of the TMD (tunned mass damper).

 

[luislb]

JBA has covered most points.
I would certainly measure the resonant frequency of the tower when the radar is not rotating. Guessing is not good enough.

If the tower is resonant close to the 60 RPM unbalance, = 1 Hz frequency, then you must change the resonant frequency of the structure. That could be done by changing the mass at the top of the tower, or by changing the height of the tower by one module, up or down.

It would also be possible to dampen the resonance by hanging a short pendulum in the top of the tower, or by having a circular tank of liquid that will dampen that resonance.

As the antenna rotates it presents maximum wind drag, twice per cycle. That could excite a 2 Hz resonance in the tower. I would expect an amplitude proportional to the square of the wind speed. Maybe that resonance is present, but is now hidden by the 1 Hz cyclic movement.

Hello Baluncore the natural frequncy of the tower assembled is 1.54 Hz ( i have a computer model). Yes the idea that change the frequency placing a water tank in the top of te tower moust likely with the form of a donut, because in the top of the platform is the pedestal of the antenna, or place the (TLD tunnde liquid damper ) underneth the platform au 45 m.

why the resonance is 2 Hz? 1 of the roatation of the tower added to a of wind grag force?

what do you think abou the analisys i´m preforming with the sofware i discribed in the JBA, answer?tank you for your help

 

[luislb]

Why is there an eccentricity? That sounds like a design defect. Have you talked with the manufacturer of this subsystem about it? Or is this a home-brew combination of the motor + antenna?

And after you get the mechanical assembly balanced better, you could still consider a cylindrical radome structure on the top of the tower to eliminate the wind effects, IMO.

https://fccid.io/png.php?id=2769752&page=7
View attachment 245413

thank you for your help, the antenna is from a danmark manufacturer, i´m sendind the caracterisctics for you, the problem is the forces/oscilation that induces in the tower.

The ideia do diminuish these effect is to place a tank of water in the top of the tower, a TLD ( Tunned liquid damper), it´s similar to the solution you recomend, how do i calibrate these cylindrical randome? it could be a great solution, although the tank of water seems to me more cheap.

Thanks

 

[luislb]

Do you have access to any of the land around the tower? Like, is it within some larger fenced-off enclosure with other equipment? If so, consider using 4 guy wires from the top of the antenna out and down to the ground to limit/eliminate the movement.

yes i can reach the tower easily because it´s near the beach, this is a thesis in civil engneering, and one of the aims it´s to place a TLD ( Tunned liquid Damper), i must place in the top of the tower a TLD to solve the problem, but thank you for the idea.

 

[Baluncore]

Consider mounting a 2D accelerometer and data logger on the tower to monitor the oscillation. You can then adjust balance weights on the rotating antenna element to reduce the imbalance.

The exciting force is at 1.0 Hz. The fundamental frequency of the tower is 1.54 Hz.
If you increase the mass at the top of the tower, you will reduce the resonant frequency. That will bring the tower resonant frequency closer to the 1 Hz driving force, which will increase the amplitude.

If, at low temperature, the liquid in the TLD became solid, resonance could then damage the tower.

why the resonance is 2 Hz? 1 of the roatation of the tower added to a of wind grag force?

The rotating antenna section, has a cyclic change in drag coefficient, at 2 * frequency of rotation.

 

[JBA]

If my analysis is correct, assuming the cause is an unbalanced rotating antenna, with your structures resonant frequency of 1.54 Hz and your antenna driving force frequency of 1 Hz (i.e. 60 rpm) you have a 1/1.54 = 0.65 forced/natural vibration ratio which for an undamped system results in a transmissibility ratio of approx 1.55 which means the oscillation (precession) amplitude of the structure would be 155% of the rotating antenna precession amplitude.
With a damping ratio of 3 you could reduce the transmissibility ratio to approx 0.25 but, as Baluncore states, if it is done by the water tank idea you add mass to the top of the tower and then freezing will eliminate your damping and the added mass will lower the natural vibration toward 1/1 in a range where small ratio changes result in rapidly increasing transmissibilty values; further, if wind becomes a factor then it is going to also change the ratio, i.e. 2/1.45 = 1.38 which moves you across the resonant 1/1 ratio point.

A combination of balancing the antenna and adding the guy wires would be well worth considering. Adding an antenna cover might also be considered but it will add the the wind drag at the top of the tower and increase the bending stress in the tower in high (storm) wind conditions so it might also require guy wires to resist those conditions.

For reference see the graph of driving/natural frequency vs. transmissibility at:
https://en.wikipedia.org/wiki/Mechanical_resonance#/media/File:Resonance.PNG

 

[berkeman]

how do i calibrate these cylindrical randome?

The radome is just to keep the wind forces off of the antenna (and to eliminate the change in the forces as the antenna rotates). It's just an RF-transparent shell.

 

[Baluncore]

High rotation rates are only needed for close range surveillance of fast targets. Coastal surveillance radar benefits from a slower scan as it looks out to 100 Nm. That becomes more true for sensitive 6+ metre long antenna arrays with a narrow beam.
So why is the antenna being operated at it's maximum specified rate of 60 RPM? Most marine radar rotates at about 26 RPM, T = 2.3 sec = 0.435 Hz. That is significantly further from the 1.58 Hz resonant frequency of the tower, so it will cause less imbalance movement.
Signal processing and digital storage displays are available, so I would ask the operators why the scanner must rotate at such a high speed. Reducing the rotation rate by a factor of two might resolve the tower oscillation problem, while increasing the radar resolution and sensitivity, and reducing the attention stress on the observer.

Designing and placing a 1 Hz TLD on the tower may psychologically lock the rotation rate to 60 RPM. That could prevent the scan rate from being reduced later to a more sensible rate with significantly improved surveillance performance.We do not know if a wind induced 2f problem is ever a significant problem during coastal hurricanes. Wind induced oscillation might become a problem if 2f came close to 1.58 Hz. That could occur when antenna rotation was close to f = 0.79 Hz = 47.4 RPM. If 2f was a problem then a symmetrical lenticular cover that rotates with the antenna element would reduce the cyclic variation in drag.

A full radome over the entire radar would not reduce the problem of the 1 Hz imbalance. As said before, it would increase the mass at the top of the tower, lowering the 1.58 Hz resonant frequency closer to the 1 Hz rotation imbalance.
Beware the Scylla and Charybdis, of a 1 Hz imbalance and a wind induced 2 Hz, while navigating a 1.58 Hz tower. In trying to reduce the 1 Hz oscillation, you may be wrecked on the 2 Hz rocks.

Engineering involves considering alternatives. If the oscillation can be reduced without a TLD, then you should get bonus marks for keeping it simple. I would solve the problem in the following order.
1. Instrument and correct the balance of the antenna.
2. Reduce the rotation rate. Learn from and educate the operators.
3. Design a TLD to remove a sufficient proportion of the remaining oscillation.
4. Evaluate the magnitude of the 2f oscillation as a function of wind speed.